A method for operating a parallel hybrid drive train of a motor vehicle is known from DE 10 2006 018 057 A1. Such a parallel hybrid drive train includes a first drive assembly formed as an internal combustion engine, a second drive assembly formed as an electric motor, a start-up element and a transmission, whereas the start-up element is connected between the electric motor and the transmission and the electric motor is connected between the internal combustion engine and the start-up element. The start-up element according to DE 10 2006 018 057 A1 includes a hydrodynamic start-up element with a converter and a lock-up clutch. In order to uncouple the internal combustion engine that is switched off, a separating clutch is connected between the internal combustion engine and the electric motor. If start-up is to occur upon an all-electric driving of the internal combustion engine, under the state of the art, it is proposed to start up the internal combustion engine by the electric motor, by at least partially closing the clutch connected between the internal combustion engine and the electric motor, whereas the lock-up clutch of the start-up element is further brought into slip, in order to guide a torque generated by the electric motor partially through the converter and partially through the lock-up clutch of the start-up element. Through the slip of the lock-up clutch of the start-up element, it is ensured that the start-up of the internal combustion engine by the electric motor has an impact on the output of the drive train in a manner that does not reduce comfort, in the form of abrupt shocks. For this purpose, according to DE 10 2006 018 057 A1, the lock-up clutch of the start-up element is held in a slip mode during the overall starting process of the internal combustion engine by rotational speed control of the electric motor. Thereby, for the start-up element, namely lock-up clutch of the same, a differential rotational speed is predetermined.
Although the method known from the state of the art provides a comfortable start-up of an internal combustion engine by an electric motor, in the case of a request for a decoupling of the lock-up clutch on the control side, there is a need to enable this decoupling within a shorter time and with greater comfort.